plantsim baby

Does the moddlet go away when they are not near the baby ?

No, it's as long as they're on the same lot

But it does go away if they are not on the same lot anymore ?

Question is if the moodlet is simply stuck or if it's something about the baby.

Have you tried resetting the baby and/or move the whole family out and back in via edit town ?

yes, I have, and I'm in a situation that I don't want to restart them

Sorry, I have no other suggestion than to wait until the baby/toddler grows up and play as is.